The dimension of the attractor for the 3D flow of a non-Newtonian fluid

M. Bulíček; F. Ettwein; P. Kaplický; Dalibor Pražák

doi:10.3934/cpaa.2009.8.1503

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2009, Volume 8, Issue 5: 1503-1520. Doi: 10.3934/cpaa.2009.8.1503

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The dimension of the attractor for the 3D flow of a non-Newtonian fluid

1.
Charles University, Faculty of Mathematics and Physics, Mathematical Institute, Sokolovská 83, 186 75 Prague 8
2.
Mathematical Institute, Charles University, Sokolovská, 83, CZ-18675 Prague 8
3.
Charles University, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Sokolovská 83, 186 75 Prague 8
4.
Department of Mathematical Analysis, Charles University, Prague, Sokolovská 83, 186 75 Prague 8

Received: July 31, 2008

Revised: December 31, 2008

Published: August 2009

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Abstract

The equations of an incompressible, homogeneous fluid occupying a bounded domain in $\mathbb R^3$ are considered.
The stress tensor has a general polynomial dependence on the symmetric velocity gradient. The goal is to estimate the dimension of the global attractor in terms of relevant physical constants.

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Mathematics Subject Classification: Primary: 38L30; Secondary: 47N10, 76A05.

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